Florida’s K – 3 Mathematics Formative Assessment System Introduction to Formative Assessment and Research Findings Laura Lang, Principal Investigator Mark LaVenia, Methodologist 2012 FCR-STEM Conference St. Petersberg, FL

Overview of presentation Introduction Definition and process Research Overview Results of MFAS studies Effect on the gender gap in 3rd grade FCAT mathematics scores Discussion

The importance of K-3 math Researchers have documented that student knowledge and achievement in mathematics in preschool and the earliest grades predicts later school success in elementary years and even through high school. Scientists typically score at the 90 th percentile or above in mathematics in high school.

The importance of K-3 math Based on an analysis using the Early Childhood Longitudinal Study of the Kindergarten Class of through 5 th grade, boys in kindergarten do better at the top of the distribution and worse at the bottom. By third grade, boys do better than girls across the distribution.

Gender Achievement Gap in Grade 3 Mathematics

Reflection and Discussion 1.What are the biggest challenges facing your teachers in elementary mathematics teaching and learning? 2.What tools do you foresee as essential to remove roadblocks for students?

Florida’s definition of formative assessment Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes. (McManus, 2008, p. 3)

Summative assessment vs. formative assessment OF Summative is an assessment OF learning. FOR Formative is an assessment FOR learning. (Black, Harrison, Lee, Marshall, & Wiliam, 2004)

What is formative assessment? A process, not a test Reveals student thinking in addition to whether or not the answer is correct Embedded within a learning activity Reveals gaps in knowledge and understanding that derail student progress Targets instruction to strengthen the core concepts and processes essential for mathematics learning Used not only to “inform” instruction, but more importantly to “form” instruction.

How does formative assessment work? Formative assessment elicits students’ thinking, helping teachers to: Diagnose critical misconceptions and errors. Identify students’ progress toward standard mastery. Differentiate instruction based on students’ understanding (i.e. individualize interventional strategies and regroup students for optimal learning opportunities). Provide students the deep understanding needed for future mathematics learning.

K-3 MFAS - CCSS tasks and rubrics For each K-3 Mathematics Common Core State Standard, there will be a minimum of four formative assessment tasks and rubrics.

Sample MFAS task Materials Instructions Background on Task

Sample MFAS rubric Misconception or Error Student Work Examples Questions Eliciting Thinking Instructional Implications

Engage Students Provide pencil, paper, base ten blocks, and number line. Ask each student to solve the following problem:

Eliciting evidence of student understanding Student solution: = 51 T: How did you get that solution? S: I added 3 and 1 to get 40. Then, I added 8 and 3 to get 11. With 40 and 11, I have 51. T: Is there any other way that you could have solved the problem? S: I don’t know, maybe. T: Will you show me what you are thinking? S: [explains another possible route]

When to implement formative assessment? Before introducing a topic, essentially identifying students’ prior knowledge After introducing a topic, with additional instructional time on the horizon

Basic formative assessment process

Select benchmark to teach Draft a sequence of tasks related to the benchmark. Implement MFAS task with student. Take notes describing each student’s response(s)— identifying gaps in knowledge. Provide descriptive feedback to students; encourage self- and peer- assessment. Develop a thorough understanding of the benchmark and related MFAS task(s). Become familiar with selected MFAS task and associated rubric. Discuss results with your team and develop a plan to differentiate instruction, targeting gaps in the student’s knowledge of the benchmark. Implement instructional plan targeted to the needs of individual students. DECISION Select a new benchmark to teach Or Implement another MFAS task related to the benchmark Or Continue instruction for student(s) who has not demonstrated mastery.

Research shows that when students take an active role in “monitoring and regulating their learning, then the rate of their learning is dramatically increased,” in fact in some instances doubled. (NCTM, 2007, p. 3) Research: Self-Assessment

In non-threatening, collaborative classroom environments: Students trust their teacher as well as their peers. Differences in ideas and opinions are respected and appreciated. Teachers exhibit model behaviors and demonstrate how to provide appropriate feedback. (Wiliam & Thompson, 2007; CCSSO, 2008) Research: Collaboration

Evaluating peer work and providing productive feedback allows students to practice and build skill in improving their own work. Effective peer assessment requires two critical elements: asin – Students must work as a group not just in a group. – Each student must be held accountable for his or her contribution to the group. (Slavin, Hurley, & Chamberlain, 2003) Research: Peer Assessment

Research: Descriptive Feedback Helps the student answer three basic questions: 1.Where am I going? 2.Where am I now? 3.How can I close the gap? Feedback should also force students to engage cognitively: 1.Find errors themselves 2.Reflect on teacher and peer feedback 3.Act on that feedback (CCSSO, 2008 )

Research: Quality Feedback  Provide students evidence-based feedback that is directly linked to the learning outcome and criteria for success.  Effective feedback needs to focus on the quality of student learning rather than on the student or the accuracy of the student’s response. VerificationVerification tells students whether or not their answers are correct. ElaborationElaboration provides information to guide students towards the correct answer. Research indicates that quality feedback should include elements of both types of feedback. (Shute, 2008)

Research: Comparative Effects Research indicates that well-designed and implemented formative assessment is an effective strategy for enhancing student learning. Intervention Extra Months of Learning Gained per Year Class-size reduction by 30% (for example, from 30 to 20 students) 3 Increase teacher content knowledge from weak to strong (2 standard deviations) 1.5 Formative assessment6 to 9 (Wiliam, 2007)

Relation between Classroom Practice and Grade 2 Student Achievement Classroom observation protocol subscale Estimate (SE)p-valueEffect Size Clarifying and sharing learning intentions 0.48 (0.11) < Eliciting evidence of learning and providing feedback 0.36 (0.13) Student self- and peer- assessment 0.25 (0.15)

MFAS Efficacy Trials Three randomized controlled trials have been conducted on MFAS: 1.a nine-week pilot study in 2010 with K-3 teacher teams using tasks aligned with Florida’s NGSSS; 2.a semester-long pilot study in 2012 with grade 2-3 teacher teams using tasks aligned with Florida’s NGSSS; and 3.a year-long study currently underway in with K-1 teacher teams using tasks aligned with the CCSS.

Study Samples 2010 nine-week pilot study – 14 schools from one district – 169 K-3 teachers – 1939 students 2012 semester-long pilot study – 21 schools across three districts – 160 grade 2-3 teachers – 2756 students

2010 MFAS - NGSS Pilot Study

2010 MFAS - NGSSS Pilot Study: Implementation Data

Other Findings from the 2010 MFAS – NGSSS Pilot Study Teachers’ knowledge of mathematics moderated the student mathematics outcomes Principal support is critical in the implementation of formative assessment. Many of the treatment group teachers initially rejected the tasks because they believed the tasks to be too difficult for students. – After implementing the tasks and seeing that their students learned to successfully solve the problems when instruction targeted the gaps in their knowledge, these teachers reported major changes in beliefs and increased expectations for students in mathematics (Lang, Schoen, Howell, & Davis, 2010).

2012 MFAS - NGSSS Pilot Study: Effect of MFAS Task Usage on Grade 2 and Grade 3 Math Performance

2012 MFAS – NGSSS Pilot Study: Effect of MFAS on Grade 3 Mathematics Achievement by Gender

MFAS-CCSS Project Development of at least 376 formative assessment tasks aligned to the CCSS for K-3 Math. Produce four introductory modules in CPALMS, three for teachers and one for school leaders. Create 18 lesson study toolkits aligned to the domains of the CCSS for K-3 Math. Test the effect of the use of MFAS on K-3 student achievement and teacher knowledge of content and pedagogy. Updates to CPALMS. All components will be available June 30, 2013.

Closing MFAS leaves teachers to decide whether tasks are implemented in one-on-one interviews, small groups, or whole class. MFAS is focused on formative assessment occurring day-to-day and minute-to-minute. MFAS is focused on teacher collaboration around student thinking and instruction. MFAS is designed to support differentiated instruction.

The 2011 – 2013 MFAS-CCSS Team Laura Lang, Principal Investigator Robert Schoen, Co-Principal Investigator Maureen Oberlin, Project Manager Michael Anderson (Pinellas) Charity Bauduin (Okaloosa) Zachary Champagne (Duval) Michelle Robinson (Seminole) Linda Walker (Walton) Andy Reeves (Pinellas) Mark LaVenia, Methodologist Anabelle Andon, ELL Support

Questions and Contact information Laura Lang, Principal Investigator